Question

An object of mass m is dropped from height h above a planet of mass M and radius R. Find an expression for the object’s speed as it hits the ground.

Answer 1

Answer:

Explanation:

Given

mass of object is m

Mass of planet is M

radius of planet is R

Total Energy associated with mass m at a height h above planet is Gravitational Potential Energy which is given by

$E_1=-\frac{GMm}{R+h}$

When it falls on earth with some velocity v

$E_2$=Kinetic Energy+Potential Energy

$=\frac{1}{2}mv^2+\frac{-GMm}{R}$

As Energy is conserved therefore

$=E_2$

$\frac{-GMm}{R+h}=\frac{1}{2}mv^2+\frac{-GMm}{R}$

$\frac{1}{2}mv^2=\frac{GMmh}{R(R+h)}$

$v=\sqrt{\frac{2GMh}{R(R+h)}}$